On policy areas in both Nevada and South Carolina, Clinton holds double-digit advantages as able to do the best job handling the economy, health care, race relations, foreign policy and climate change, according to the poll.

She's also seen by 58 percent in South Carolina, and 59 percent in in Nevada, as being the candidate with the best chance to win in 2016.

But when it comes to honesty and trustworthy, the poll finds in South Carolina, support breaks:

Clinton: 35 percent

Biden: 27 percent

Sanders: 21 percent

On those same qualities, in Nevada, the support breaks:

Sanders: 33 percent

Clinton: 32 percent

Biden: 22 percent

The margin of error in South Carolina is 5.5 percentage point; for Nevada, it's 6 points.